Chapter 11: Problem 49
Chloroform, \(\mathrm{CHCl}_{3}\), a volatile liquid, was once used as an anesthetic but has been replaced by safer compounds. Chloroform boils at \(61.7^{\circ} \mathrm{C}\) and has a heat of vaporization of \(31.4 \mathrm{~kJ} / \mathrm{mol}\). What is its vapor pressure at \(37.2{ }^{\circ} \mathrm{C} ?\)
Short Answer
Step by step solution
Understanding the Clausius-Clapeyron Equation
Convert Temperatures to Kelvin
Calculate the Heat of Vaporization in J/mol
Assume Initial Pressure and Find New Pressure Ratio
Solve for the New Vapor Pressure, \(P_2\)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Vapor Pressure
Understanding vapor pressure is crucial, as it impacts how a liquid behaves under different conditions. Liquids with high vapor pressure evaporate more easily at a given temperature.
- Vapor pressure increases with temperature because more molecules have enough energy to escape the liquid phase.
- Saturation occurs when the vapor pressure equals the atmospheric pressure, leading to boiling.
Heat of Vaporization
In the case of chloroform, the heat of vaporization is given as 31.4 kJ/mol. To use this value in calculations, often it's essential to convert it to other units, such as J/mol, because scientific equations frequently use these units.
- The conversion involves multiplying by 1,000 (since 1 kJ = 1,000 J).
- In our problem, this results in a heat of vaporization of 31,400 J/mol.
- This value is crucial in computing changes in vapor pressure with the Clausius-Clapeyron equation.
Temperature Conversion
The Kelvin scale starts at absolute zero, making it ideal for scientific work. To convert Celsius to Kelvin, simply add 273.15 to the Celsius temperature.
- For example, converting 61.7°C, the boiling point of chloroform, results in 334.85 K.
- Similarly, a temperature of 37.2°C becomes 310.35 K when converted to Kelvin.
Gas Constant
This constant links the physical properties of gases with temperature, pressure, and volume. It is used prominently not only in the Clausius-Clapeyron equation but also in the Ideal Gas Law: PV = nRT.
- In our context, it enables the calculation of the change in pressure with temperature, relating to the heat of vaporization of the substance.
- This constant aids in balancing energy and matter transformation calculations across various equations.